标题： 一维金属量子线在各种约束下的相关效应 显示英文标题

标题： Correlation effects in one-dimensional metallic quantum wires under various confinements

摘要： 动态响应理论用于研究不同线宽$b$和密度参数$r_{\rm s}$的铁磁一维量子线基态中电子关联的各种横向限制。使用一阶随机相位近似 (FRPA)，该方法提供了超越随机相位近似的基态结构，我们计算了结构因子、对关联函数、关联能和基态能量。关联能取决于限制模型的选择，因此有效电子-电子相互作用也有所不同。对于高密度极限下的超薄线 ($b\rightarrow 0$)，横向限制模型$V_1(q)$(谐波)、$V_2(q)$(圆柱形) 和$V_5(q)$(谐波-δ) 的关联能接近$\epsilon_{\rm c}(r_{\rm s})= - \pi^2/360 \sim -0.02741$a.u.，这与该极限下的精确结果一致 [J. Chem. Phys. 138, 064108 (2013); Phys. Rev. B 101, 075130 (2020)]。 对于至少这三个约束势，一维库仑势可以在粒子间距离$x=0$处进行正则化，以得到相同的关联能。 相反，$V_3(q)$（无限深方势阱）、$V_4(q)$（无限深方势阱-无限深三角势阱）和$V_6(q)$（无限深方势阱-δ势阱）不趋近于相同的高密度极限；相反，关联能趋于$\epsilon_{\rm c} \sim -0.03002$a.u。 从 FRPA 得到的基态性质与量子蒙特卡罗结果进行了比较。 静态结构因子在$k=2k_{\rm F}$处的峰值高度显著依赖于约束模型。 这些峰值通过基于我们有限线宽理论的函数进行拟合，显示出与 FRPA 的良好一致性。 显示英文摘要

摘要： Dynamical response theory is used to investigate various transverse confinements on electron correlations in the ground state of a ferromagnetic one-dimensional quantum wire for different wire widths $b$ and density parameters $r_{\rm s}$. Using the first-order random phase approximation (FRPA), which provides the ground state structure beyond the random phase approximation, we compute the structure factor, pair-correlation function, correlation energy, and ground-state energy. The correlation energy depends on the choice of confinement model and hence effective electron-electron interaction. For the ultrathin wire ($b\rightarrow 0$) in the high-density limit, the correlation energy for transverse confinement models $V_1(q)$ (harmonic), $V_2(q)$ (cylindrical), and $V_5(q)$ (harmonic-delta) approaches $\epsilon_{\rm c}(r_{\rm s})= - \pi^2/360 \sim -0.02741$ a.u., which agrees with the exact results in this limit [J. Chem. Phys. 138, 064108 (2013); Phys. Rev. B 101, 075130 (2020)]. For at least these three confinement potentials, the one-dimensional Coulomb potential can be regularized at interparticle distance $x=0$ to yield the same correlation energy. In contrast, $V_3(q)$ (infinite square well), $V_4(q)$ (infinite square-infinite triangular well), and $V_6(q)$ (infinite square-delta well), do not approach the same high-density limit; instead, the correlation energy tends to $\epsilon_{\rm c} \sim -0.03002$ a.u. The ground-state properties obtained from the FRPA are compared with quantum Monte Carlo results. The peak height in the static structure factor at $k=2k_{\rm F}$ depends significantly on the confinement model. These peaks are fitted with a function based on our finite wire-width theory demonstrating good agreement with FRPA.